Question

For a black body at temperature ${727}^o$ its rate of energy loss is $20$ watt and temperature of surrounding is ${227}^{o}C$. If temperature of black body is changed to ${1227}^C$ then its rate of energy loss will be:

• A. $304W$
• B. $\frac{320}{3}W$
• C. $240W$
• D. $120W$

Answer 1

Answer: (B)

$\frac{320}{3}W$

$\frac{P_2-20}{20}=\frac{{1500}^4-{1000}^4}{{1000}^4-{500}^4}$
$\frac{P_2}{20}-1=\frac{50625\times {10}^8-10000\times {10}^8}{10000\times {10}^8-625\times {10}^8}$
$\frac{P_2}{20}-1=\frac{40625\times {10}^8}{9375\times {10}^8}$
$\frac{P_2}{20}-1=\frac{40625}{9375}=\frac{13}{3}$
$\frac{P_2}{20}=\frac{13}{3}+1=\frac{16}{3}$
$P_2=\frac{16\times 20}{3}=\frac{320}{3}W$